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On the C 1 continuous discretization of non‐linear gradient elasticity: A comparison of NEM and FEM based on Bernstein–Bézier patches

2009; Wiley; Volume: 82; Issue: 10 Linguagem: Inglês

10.1002/nme.2802

1097-0207

Paul Fischer, Julia Mergheim, Paul Steinmann,

Numerical methods in engineering

Abstract In gradient elasticity, the appearance of strain gradients in the free energy density leads to the need of C 1 continuous discretization methods. In the present work, the performances of C 1 finite elements and the C 1 Natural Element Method (NEM) are compared. The triangular Argyris and Hsieh–Clough–Tocher finite elements are reparametrized in terms of the Bernstein polynomials. The quadrilateral Bogner–Fox–Schmidt element is used in an isoparametric framework, for which a preprocessing algorithm is presented. Additionally, the C 1 ‐NEM is applied to non‐linear gradient elasticity. Several numerical examples are analyzed to compare the convergence behavior of the different methods. It will be illustrated that the isoparametric elements and the NEM show a significantly better performance than the triangular elements. Copyright © 2009 John Wiley & Sons, Ltd.